An improved model for the kinetic description of the thermal
degradation of cellulose
Pedro E. Sánchez-Jiménez1 , Luis A. Pérez-Maqueda1, Antonio Perejón1, José Pascual-Cosp2,
Mónica Benítez-Guerrero2 and José M. Criado1
(1) Instituto de Ciencia de Materiales de Sevilla, C.S.I.C.-Universidad de Sevilla, C. Américo
Vespucio no 49, 41092 Sevilla, Spain
(2) Departamento de Ingeniería Civil, Materiales y Fabricación, Universidad de Málaga, ETSII,
29071 Málaga, Spain
Abstract
In spite of the large amount of work performed by many investigators during last decade, the
actual understanding of the kinetics of thermal degradation of cellulose is still largely
unexplained. In this paper, recent findings suggesting a nucleation and growth of nuclei
mechanism as the main step of cellulose degradation have been reassessed and a more
appropriate model involving chain scission and volatilization of fragments has been proposed
instead. The kinetics of cellulose pyrolysis have been revisited by making use of a novel kinetic
method that, without any previous assumptions regarding the kinetic model, allows
performing the kinetic analysis of a set of experimental curves recorded under different
heating schedules. The kinetic parameters and kinetic model obtained allows for the
reconstruction of the whole set of experimental TG curves.
Keywords
Kinetics – Cellulose – Thermal degradation – Chain scission
Introduction
Cellulose is the most abundant biopolymer on earth and, together with hemicellulose and
lignin, is one of the main three constituents of biomass, which is being increasingly considered
as fuel or source for renewable energy (Saddawi et al. 2010; Emsley 2008) Thermal
decomposition of biomass can also be used for the production of chemicals and bio-oils
(Mohan et al. 2006). Moreover, due to its availability, low cost and biodegradability, cellulose
is more and more used to reinforce polymeric materials and to design a huge array of novel
biopolymers and biocomposites (Liu et al. 2010; Ganster and Fink 2006). The accurate
modeling of the thermal degradation kinetics is vital for the control of combustion processes,
for the thermal characterization of newly designed biocomposites and for the assessment of
possible damage during processing.
The degradation of cellulose has attracted a great deal of attention during the last decade
(Bigger et al. 1998; Volker and Rieckmann 2002; Mamleev et al. 2006; Capart et al. 2004; Shen
and Gu 2009; Mamleev et al. 2007a, b; Lin et al. 2009; Ding and Wang 2008b; Calvini et al.
2008). Cellulose can be degraded under thermal, oxidative, hydrolytic or enzymatic conditions;
in every case yielding sugar fragments of varying length due to the scission of polymeric chains.
Thus, the degradation process can be characterized by following the evolution of the chain
scissions and the degree of polymerization with time, usually utilizing kinetic equations derived
from the first or pseudo-zero order Ekenstam’s relationship (Emsley 2008; Calvini et al. 2008;
Ding and Wang 2008b; Calvini 2005, 2008; Ding and Wang 2008a). These studies are usually
1
supported by experimental data obtained from cellulose degradation by hydrolysis or thermal
ageing at low temperatures. However, since the scission of bonds is not a variable easy to
measure directly, the thermal degradation of cellulose is instead often studied by monitoring
the weight loss endured during thermogravimetric experiments at high temperatures (250–
400 °C), where the evolution of the degradation process can be followed in situ. This approach
has produced an important body of work and it is generally acknowledged now that cellulose
decomposes through parallel or competitive reactions, producing tar, gases and residual char
(Shen and Gu 2009; Capart et al. 2004; Mamleev et al. 2009; Mamleev et al. 2007a, b). Many
authors have proposed single step first order models to describe the kinetics of cellulose
decomposition, (Varhegyi et al. 1994; Antal et al. 1998) while others like Agrawal or Bradbury
(Bradbury et al. 1979; Agrawal 1988a, b) have resorted to multistep kinetic pathways. These
multistep models assume several consecutive or competitive pathways, as suggested by the
fact that the amount and type of volatiles and the residual char distinctly depend on the
heating rate used in the experiments (Mamleev et al. 2007a; Kilzer and Broido 1965).
However, the formation of “active cellulose” and other intermediates assumed in several
multistep models remains controversial because such products are difficult to identify and
quantify (Shen and Gu 2009; Capart et al. 2004; Lin et al. 2009). Also, the use of sophisticated
multistep kinetic models involves a high number of fitting parameters that will inevitably lead
to an acceptable fit of the experimental data, regardless the validity of such model.
Furthermore, for the sake of simplicity the individual steps are all usually assumed to obey first
order kinetic laws, what might easily constitute an oversimplification. Nevertheless, most
authors still consider that complex multistep models are not needed to simulate the weight
loss behavior during the pyrolysis of cellulose, and that single step models are sufficient to
describe the system adequately since “depolymerization by transglycosylation”, namely the
scission of the internal glycosidic bonds, has been reported to be the limiting step (Varhegyi et
al. 1994; Mamleev et al. 2006). Within the single step models, first order (Varhegyi et al. 1994;
Antal et al. 1998; Shen and Gu 2009) or nth order kinetics (Barneto et al. 2009) are still
assumed in the majority of the situations. However, some authors have recently found
autoaccelerated models such as Avrami-Erofeev or Prout-Tompkins, which are commonly
related to nucleation and growth mechanisms, to be a better depiction (Dollimor and Holt
1973; Reynolds and Burnham 1997). More recently, Mamleev (Mamleev et al. 2007a) and
Capart (Capart et al. 2004) confirmed that nucleation models are far more suited than the so
often used first order models. In his work, Capart (Capart et al. 2004) assumed two
independent reactions; one related to the bulk decomposition of cellulose and a second one
related to a much slower residual decomposition. Alternatively, Mamleev (Mamleev et al.
2006) proposed a two step kinetic model that described the mass loss by two competing
pathways; a dominant “depolymerisation by transglycosilation” reaction producing tar, and an
elimination reaction that produces char and light gases.
Thus, despite the huge amount of work published, the kinetics of cellulose pyrolysis
constitutes a topic still profusely under debate. It is a complex process involving complicated
chemical pathways, mass and heat transfer phenomena and possible intermediates. As a
consequence, there is a large variation in the magnitude of activations energies published for
describing the reaction (Antal et al. 1998; Capart et al. 2004; Lin et al. 2009). This dispersion
has been attributed mainly to thermal lag and uncontrolled heat transfer issues, (Antal et al.
1998; Lin et al. 2009) and to the different morphologies and crystallinities of the studied
samples (Capart et al. 2004; Antal et al. 1998). The influence of different initial sample sizes on
the products yielded by experiments carried out under similar thermal treatments has shown
the importance of heat transfer in this process (Volker and Rieckmann 2002; Shen and Gu
2009). An alternative explanation for the dispersion of results could lie in the fact that most
kinetic studies are performed using model-fitting methods, consisting on fitting the
experimental curves to different mathematical models, described based on certain physico2
geometrical assumptions. This approach entails an often overlooked limitation: the kinetic
parameters thus obtained are highly dependent on the kinetic model assumed. Thus, since any
list of kinetic models is inevitably incomplete, the best fit in a set does not necessarily imply
that the selected model is the right one. Additionally, in many cases the kinetic models are
used merely as fitting equations and hence they grant no further understanding of the
degradation mechanism (Capart et al. 2004; Barneto et al. 2009).
In this work, a non conventional kinetic analysis procedure (Perez-Maqueda et al. 2006; Criado
et al. 2003; Perez-Maqueda et al. 2003) has been applied to cellulose decomposition in order
to shed new light to the process. The recently proposed combined kinetic analysis is a method
that allows for the simultaneous analysis of a set of experimental curves recorded under any
thermal schedule, and more importantly, without any previous assumption about the kinetic
model followed by the reaction. This constitutes an important improvement over the most
commonly used model fitting methods because, unlike them, combined kinetic analysis does
not constrain the experimental data into a predefined kinetic model. The results, obtained
from the combined analysis of experimental data recorded under isothermal, linear heating
and Constant Rate Thermal Analysis (CRTA) conditions, are compared with the most widely
used kinetic models in literature, including a recently proposed one for chain scission
mechanisms, which seems especially well suited to the case of cellulose degradation.
Experimental
Commercial microcrystalline cellulose from Aldrich, (product number 435236) was used for
performing the study. Thermogravimetric measurements were carried out with a TA
instruments Q5000 IR electrobalance (TA Instruments, Crawley, UK) connected to a gas flow
system to work in inert atmosphere (150 mL min−1 N2). The experiments were performed with
the utmost care in order to minimize heat and mass transfer phenomena so that kinetic
parameters more representative of the forward reaction are obtained. Small initial mass
samples (8–10 mg) were placed over a 1 cm diameter platinum pan. The sample was well
dispersed and with negligible depth in order to minimize heat and mass transfer phenomena,
along with possible secondary carbon yielding reactions, by reducing the residence time of the
volatiles within the solid (Capart et al. 2004). Experimental data were obtained from
experiments run under three different heating schedules: isothermal conditions, linear heating
rate and Constant Rate Thermal Analysis (CRTA). This method implies controlling the
temperature in such a way that the reaction rate is maintained constant all over the process at
a value previously selected by the user. Isothermal experiments were carried out at 533 and
548 K. Four different heating rates, 1, 2, 5 and 10 K min−1 were used for experiments run under
linear rise in temperature. The α-T (or time) plots obtained from these two methods were
differentiated by means of the Origin software (OriginLab) to get the differential curves
employed in the kinetic analysis. Finally, CRTA experiments were performed at constant
reactions rates of 0.006 and 0.009 min−1, respectively.
Theory
Theoretical background
The reaction rate, dα/dt, of a solid state reaction can be described by the following general
equation:
(1)
3
where A is the Arrhenius pre-exponential factor, R is the gas constant, E the activation energy,
α the reacted fraction, T is the process temperature and f(α) accounts for the reaction rate
dependence on α. The kinetic model f(α) is an algebraic expression which is usually associated
with a physical model that describes the kinetics of the solid state reaction. Table 1 lists the
functions corresponding to the most commonly used mechanisms found in literature. In this
work, the reacted fraction, α, has been expressed with respect to the degradable part of the
cellulose, as defined below:
(2)
where w o is the initial mass of cellulose, w f the mass of residual char and w the sample mass
at an instant t.
Equation 1 is a general expression that describes the relationship among the reaction rate,
reacted fraction and temperature independently of the thermal pathway used for recording
the experimental data. For experiments performed under isothermal conditions, the sample
temperature is rapidly increased up to a certain temperature and maintained at this
temperature while the reaction evolution is recorded as a function of the time. Under these
experimental conditions, at a given temperature T, the term A exp(−E/RT) remains constant at
a value k T , and therefore, Eq. 1 can be written as follows:
(3)
Sample Controlled Thermal Analysis (SCTA) constitutes an alternative approach that, while
amply used in solid state kinetic studies and preparation of materials (Rouquerol 2003; PerezMaqueda et al. 1999), it has only recently extended to polymer decomposition reactions
(Sanchez-Jimenez et al. 2009, 2010c; Sanchez-Jimenez et al. 2010a; Arii et al. 1998). In SCTA
experiments, the evolution of the reaction rate with time is predefined by the user and, most
usually, it is maintained at a constant value along the entire process. In this case, the technique
is named Constant Rate Controlled Analysis (CRTA). This way, by selecting a low enough
decomposition rate, the mass and heat transfer phenomena occurring during the reaction are
minimized. This is a very useful asset when dealing with complex reactions such as cellulose
pyrolysis, which has proven to be very susceptible to mass and heat transfer phenomena
(Volker and Rieckmann 2002; Lin et al. 2009). As a consequence, the results obtained by CRTA
are more representative of the forward reaction than those obtained from conventional
methods such as linear heating programs or isotherms (Koga and Criado 1998; Rouquerol
2003; PerezMaqueda et al. 1996). Under constant rate thermal analysis (CRTA) conditions, the
reaction rate is maintained at a constant value C = dα/dt selected by the user and Eq. 1
becomes:
(4)
Isoconversional analysis
Isoconversional methods, also known as “model-free”, are used for determining the activation
energy as a function of the reacted fraction without any previous assumption on the kinetic
model fitted by the reaction. The Friedman isoconversional method is a widely used
differential method that, unlike conventional integral isoconversional methods, provides
accurate values of the activation energies even if they were a function of the reacted fraction
(Criado et al. 2008). Equation 1 can be written in logarithmic form:
4
(5)
At a constant value of α, f(α) would also be constant and Eq. 5 could be written in the form:
(6)
The activation energy at a constant α value can be determined from the slope of the plot of
the left hand side of Eq. 5 against the inverse of the temperature, at constant values of α.
Combined kinetic analysis
The logarithmic form of the general kinetic Eq. 1 can be rewritten as follows:
(7)
The plot of the left hand side of the equation versus the inverse of the temperature will yield a
straight line if the proper f(α) is considered for the analysis (Perez-Maqueda et al. 2003). The
activation energy can be calculated from the slope of such plot, while the intercept leads to
the pre-exponential factor. As no assumption regarding the thermal pathway is made in Eq. 7,
the kinetic parameters obtained should be independent of the thermal pathway. Thus, this
method would allow for the simultaneous analysis of any set of experimental data obtained
under different thermal schedules (Perez-Maqueda et al. 2006). To overcome the limitation
related to the fact that the f(α) functions were proposed assuming idealized physical models
which may not be necessarily fulfilled in real systems, a new procedure was introduced in a
recent work, where the following f(α) general expression was proposed (Perez-Maqueda et al.
2006).
(8)
This equation is a modified form of the Sestak-Berggren empirical equation (Sestak and
Berggren 1971). It has been shown that it can fit every function listed in Table 1 by merely
adjusting the parameters c, n and m. Consequently, Eq. 8 effectively works as an umbrella that
covers the most common physical models and its possible deviations from ideal conditions.
From Eqs. 7 and 8 we reach:
(9)
The Pearson linear correlation coefficient between the left hand side of the equation and the
inverse of the temperature is set as an objective function for optimization. By means of the
maximize function of the software Mathcad, the parameters n and m that yield the best linear
correlation are obtained, and the corresponding values of E and A are calculated (PerezMaqueda et al. 2006). Nevertheless, it should be noted that the combined analysis approach
rest in the assumption that the reaction can be described by a single set of kinetic parameters
and, consequently, a single activation energy.
5
Kinetic model for random chain scission reactions
Considering that a polymer degrades through the cleavage of bonds following first order
kinetics (Simha and Wall 1952), the following expressions hold true:
(10)
(11)
where x, N and L are the fraction of bonds broken, the initial degree of polymerization and the
minimum length of the polymer that is not volatile, respectively.
As L is usually negligible in comparison to N, Eq. 11 can be simplified to:
(12)
The model assumes all breakable bonds within the polymer to be equal (no weak links) and
therefore, all have the same probabilities to be broken. Hence the term “random.” In
thermogravimetric experiments the mass lost constitutes a direct measure of the reacted
fraction. However, when dealing with chain scission reactions, only the broken bonds that lead
to fragments which are small enough to evaporate will actually be detected as mass lost.
Therefore, a relationship between the detected mass loss and the actual reacted fraction must
be established before the equations can be used. That can be achieved by means of Eq. 12,
which relates the reacted fraction α in terms of mass lost (as recorded during a
thermogravimetric experiment) with the fraction of bonds broken (Sanchez-Jimenez et al.
2010c). However, as x cannot be measured by conventional techniques, and L is very difficult
to determine experimentally, the application of Eq. 12 is severely limited. Nevertheless, by
differentiating Eq. 12, and incorporating Eq. 10 we get:
(13)
This way, taking into account Eq. 1, we can deduct the conversion function f(α) that describes a
random scission model:
(14)
Unfortunately, a symbolic solution can only be reached for L = 2, which is included in Table 1.
Nevertheless, taking into account that the relationship between x and α is already established
in Eq. 12, for any given L and assigning values to α, from Eqs. 12 and 14 it is easy to calculate
numerically the f(α) conversion functions corresponding to any L values. The resulting f(α)
functions for different L values have been developed in detail elsewhere (Sanchez-Jimenez et
al. 2010c), but it is worth mentioning out here that they all show a minimum in the T-α plots at
α values of around 0.25.
Results and discussion
Kinetic study of the thermal degradation of cellulose under different heating schedules
6
Figure 1 shows the experimental α-T curves recorded for the thermal degradation of
microcrystalline cellulose under linear heating rate (1a), isothermal (1b) and CRTA (1c)
conditions. Experiments under linear heating rate conditions have the typical sigmoidal shape
that is obtained for any kinetic curve when recorded under this heating schedule. For that
reason it is not possible to obtain information about the kinetic mechanism directly from the
shape of the experimental curves recorded under linear heating conditions (Criado and
Morales 1976, 1977; Perez-Maqueda et al. 2002b).
Isothermal experiments were performed by quickly heating up to the target temperature to
avoid mass loss during the heating. The majority of the mass loss takes place during the
isothermal part of the experiment and the degradation during the heating up is negligible. The
experimental isothermal curves (Fig. 1b) have a sigmoidal shape with an inflection point in the
initial stages of the degradation, which is indicative of an “acceleratory” type model such as
nucleation or chain scission. The plot of the reaction rate, dα/dt, against the conversion, α, for
both isotherms (Fig. 2) can be very illustrative in these situations because under isothermal
conditions the term A exp(−E/RT) becomes constant (Eq. 3) and, therefore, the shape of the of
plot depends exclusively on the kinetic model obeyed by the reaction. The plots in Fig. 2
display a maximum in the reaction rate at around α = 0.23–0.24.
In Fig. 3, the CRTA curve obtained at a constant rate of 0.009 min−1 is presented as an example
of the kind of experimental curves obtained under constant rate experimental conditions. Both
the temperature and the reacted fraction are plotted as a function of time as directly recorded
by the instrument. The temperature rises until reaching the constant reaction rate previously
selected. Then, the experimental arrangement forces α to fit a straight line as a function of the
time. It has been proven that CRTA experiments provide a much better resolution power for
discriminating the kinetic model obeyed by the reaction since the shape of the T-α is intimately
related to the kinetic model (Sánchez-Jiménez et al. 2011; Sanchez-Jimenez et al. 2010b; PerezMaqueda et al. 2002a). Thus, valuable information can be extracted from the shape of
decomposition curves regarding the nature of the reaction. In the inset in Fig 3 it can be seen
that the T-α plot exhibits a minimum at α values of around 0.25, what has been reported to be
characteristic of chain scission driven processes (Sanchez-Jimenez et al. 2010c).
Table 2 lists the activation energy as a function of the conversion calculated by means of the
Friedman isoconversional analysis, as detailed in “Isoconversional analysis”. All experimental
curves included in Fig. 1, run under isothermal, linear heating and CRTA conditions, were
analysed simultaneously. These results show that cellulose pyrolysis can be described by a
single activation energy of 191 kJ mol−1 up to α = 0.9. From that point, there is a significant
deviation, maybe due to the existence of a second process which contribution to the overall
reaction rate only gets significant at high conversion values. The resulting activation energy
values from α = 0.9 onward are no longer reliable as suggested by the large standard error and
poor correlation factors. This result, indicating that the thermal pyrolysis of cellulose involves
two processes, is in agreement with literature data (Shen and Gu 2009; Capart et al. 2004;
Mamleev et al. 2009; Mamleev et al. 2007a, b). However, the second process has a very
limited contribution to the overall reaction, and only at very high conversion values.
Consequently, a detailed kinetic description of the entire process becomes very complex since
the second reaction involves a very small fraction of the total weight loss and occurs during
extended times. Capart (Capart et al. 2004) approached the system by considering two
independent reactions that affected a different fraction of the initial cellulose, estimating an
activation energy of 250 kJ mol−1 and a kinetic model f(α) = α 22(1−qα) for the second, much
slower, reaction. However, the physical meaning of such kinetic model is difficult to grasp.
Since the presence of traces of oxygen remnants in the system is extremely difficult to avoid,
7
this second process in cellulose degradation could be related with the volatilization due to
oxidation of the residual char produced during the degradation and remains in the balance. At
higher temperatures this process would be favoured, resulting in a smaller residual char in the
experiments carried out at higher heating rates. This varying percentage of overall mass lost
with the heating rate would explain the difficulties at fitting the very last part of the conversion
range. Since this study focus on the main process that constitutes the cellulose thermal
degradation, only the experimental data below α = 0.9 will be considered with regards to
determining the kinetic parameters. Also, no further hypothesis upon the nature of the
chemical reactions and the products is made.
The activation energy calculated by means of the isoconversional method was found to be
constant in all the considered range. Thus, the entire reaction can be described by a single
activation energy. All the curves included in Fig. 1, independently of the heating conditions
under which they were obtained, were simultaneously analysed as described in “Combined
kinetic analysis”. Figure 4 shows the plot of the values calculated for the left hand side of Eq. 9
using the whole set of experimental data versus 1/T. As expected, the entire conversion range
could not be successfully fitted to a straight line, showing important deviation from linearity at
the very high end of conversion values, due to the aforementioned second process, which
responds to a different kinetic mechanism. Therefore, in order to focus exclusively in the main
decomposition step, the experimental data over α = 0.9 are discarded. Figure 4 demonstrates
that experimental data up to α = 0.9 are fitted to a single straight line when a modified SestakBerggren equation with n = 1.300 and m = 0.392 is used as f(α). The correlation coefficient is
0.998. The slope of the plot leads to an activation energy value of 193.3 ± 0.4 kJ mol−1 and the
intercept to an Arrhenius pre-exponential factor of (5.9 ± 0.5) 1016 min−1. The activation energy
is in agreement with the values calculated using Friedman isoconversional analysis and similar
to those proposed by other authors that used a Prout-Tompkins type equation to fit the
experimental data (Capart et al. 2004; Antal et al. 1998; Mamleev et al. 2006). It is important
to point out that the conversion function f(α) estimated by combined kinetic analysis presents
no physical meaning by itself. Thus, comparison with the theoretical kinetic functions listed in
Table 1 is needed in order to determine the kinetic model the reaction follows. In Fig. 5 the
conversion function estimated by combined kinetic analysis, that is f(α) = α0.392(1−α)1.3, is
plotted together with some of the most widely used kinetic models in literature, such as
nucleation and growth, first order, diffusion controlled, and the chain scission model described
in “Kinetic model for random chain scission reactions”. The comparison in Fig. 5 evidences that
the estimated f(α) clearly resembles a chain scission mechanism with only a small deviation
with respect to the theoretical curve. This is expected because the kinetic models were
proposed assuming ideal conditions that are difficult to fulfill in real systems. It is noteworthy
to remark that this conclusion has been reached without any previous assumption regarding
the kinetic model or the activation energy. This finding is consistent with the observations
made from the position of the minimum in the T- α curve recorded for the CRTA experiment,
which also points towards a chain scission model as the most probable for the studied
reaction. The reconstruction of curves is a useful method for validating the kinetic parameters
obtained by a kinetic analysis. Here, a set of curves has been simulated assuming the kinetic
parameters obtained from the combined kinetic analysis and heating conditions identical as
those used in the experiments. The simulations were performed by means of a 4th order
numerical integration Runge–Kutta method; using Eq. 1 and the equations that define the
heating conditions, i.e. linear heating, isothermal (Eq. 3) and constant rate (Eq. 4). As Fig. 1
shows, both the reconstructed (simulated) curves and the experimental ones match exactly for
values of α up to 0.9, proving the validity of the kinetic parameters obtained from the
combined analysis. The fact that curves carried out under different heating schedules can all
be reconstructed with the same kinetic parameters indicates that mass and heat transfer
influence have been successfully suppressed from the experiments since the different heating
conditions are expected to affect the reaction in different ways.
8
Evaluation of the use of first order and nucleation models for the kinetic description of
cellulose degradation
It is well known that the proper kinetic description of a process requires the knowledge of the
so called kinetic triplet; namely the activation energy, the preexponential factor and the kinetic
model. The latter is especially important since many kinetic analysis methods are based upon
fitting the experimental data to a previously assumed kinetic model. Therefore, since the
kinetic parameters yielded by a model-fitting method are intimately related with the kinetic
model assumed, fitting the experimental data to an incorrect model will lead to incorrect
kinetic parameters. Also, since no list of models is absolute, the best fit in a limited set of
models does not guarantee the correctness of such model. The most widely proposed single
step models in literature for describing the thermal degradation of cellulose are first order and
autoacceleratory models such as Avrami-Erofeev or Prout-Tompkins. The suitability of such
models is analyzed in this section. A careful look at the functions in Fig. 5 reveals that the first
order kinetic model (F1) and the chain scission models described in “Kinetic model for random
chain scission reactions” (L2 and L8) are almost identical from α = 0.4 onwards. This fact could
explain why several authors have considered first order models satisfactory enough to
describe cellulose pyrolysis. The fit of the experimental data to a first order model would be of
acceptable quality in a range of conversions starting α = 0.4, and would yield an activation
energy close enough to the values proposed in literature. However, as it has been
demonstrated elsewhere (Sanchez-Jimenez et al. 2010c; Sánchez-Jiménez et al. 2011), first or
“n order” laws could never reproduce the initial induction or acceleratory period detected in
both isothermal and CRTA experiments (Figs. 2, 3) because the equations that describe those
laws simply do not allow so. Consequently, any attempt to reconstruct the degradation curves
assuming a first order law, or even to predict the behavior of cellulose in conditions different
from the experimental ones, will inevitably prove unsuccessful. The initial acceleratory period
entails important consequences at the practical level. If any cellulose derived material
undergoes heating at a temperature high enough during processing, recycling or any other
application, it might be possible that the depolymerization process is started, even if no
significant mass loss is detected. Any subsequent temperature treatment could speed up the
degradation since the fragmentation of cellulose chains had already begun.
Capart (Capart et al. 2004) found that thermogravimetric curves obtained from cellulose
pyrolysis could be fitted by a “first order Sestak-Berggren nucleation model” under the form
f(α) = α(1−qα)0.481, and determined it was equivalent to an Avrami-Erofeev model with n
exponent of around 1.5. In principle, an Avrami-Erofeev mechanism with an exponent n equal
to 1.5 encompasses two possible physico-geometrical situations: either an instantaneous
nucleation followed by a diffusion-controlled three-dimensional growth of nuclei, or a
diffusion-controlled one-dimensional growth following a constant rate homogeneous
nucleation (Perez-Maqueda et al. 2003). Since Avrami-Erofeev models were proposed for the
description of nucleation driven processes, some authors have recently postulated
degradation mechanisms based on nucleation and growth of nuclei for describing cellulose
decomposition. As an example, Mamleev et al. (2007b; 2009) have speculated with a twophase model that tries to explain the nucleation mechanism with the appearing of microscopic
droplets of boiling tar that forms within the cellulose matrix and eventually grow due to
migration of chain ends to the interface liquid–solid.
Actually, the main reason why authors have considered nucleation models for describing
cellulose pyrolysis is just because “acceleratory” conversion functions provided the best fit to
the experimental data. However, the thermal degradation of polymer-like materials has very
rarely been found to proceed through a nucleation mechanism. Only a recent study about the
9
dehydrochlorination of PVC, what constitutes the first step of PVC thermal degradation, has
been found (Sanchez-Jimenez et al. 2010a, b). Even in such a case, the mass loss during the
dehydrochlorination is due to the release of side groups with different tacticities so no actual
scission of the polymeric backbone is actually involved in the process. In the case of cellulose
pyrolysis, the major cause of mass loss in thermogravimetry is most probably the
fragmentation of cellulose chains, a situation that is not easily rationalized with a nucleation
model.
Chain scission as the most suitable kinetic model for describing the thermal degradation of
cellulose
Figure 5 evidences that random scission kinetic models better approximate the experimental
curves than the aforementioned Avrami-Erofeev models. Moreover, not only a better fit to the
experimental data is provided, but also a more adequate physical description of the reaction
since the basis of the model rest in the breakage of polymeric chains. The physical meaning of
such model can be more easily comprehended by following the CRTA curve in Fig. 3 and the
graphical description in Fig 6. The mass loss that accompanies the degradation during a TG
experiment can be ascribed to the evaporation of short fragments, which are most probably
released after breakages close to the chain endings. The chances for those events are much
slimmer during the initial reaction times (Step 1 in Fig. 6) when the cellulose chains are still
long and the fragments resulting from the scissions are not short enough to evaporate. Thus,
as the predetermined reaction rate for the CRTA experiment is not yet achieved, the
temperature keeps rising. At Step 2, when the cellulose chains are sufficiently fragmented,
even if the rate of bond scission is the same, a greater fraction of the scissions will produce
volatilization. Therefore, the rate of mass loss suddenly raises and the temperature must drop
to reduce the rate of bonds broken (Step 3) in order to maintain the reaction rate, as reflected
by the rate of mass loss, constant. Therefore, like nucleation and growth mechanisms, chain
scission is also acceleratory in nature as it can be observed in both isothermal and CRTA
experiments. It should be noted that thermogravimetric experiments are only sensitive to
mass loss, and recombination reactions between volatiles are not detected. In the same way,
chain breakages leading to tar would neither be detected until the tar ulterior volatilization.
A careful look at f(α) functions plotted in Fig. 5 reveals some likeness between the curves
corresponding to random scission and to Avrami-Erofeev when n = 1.5. This could have led to a
misinterpretation of the kinetics of cellulose degradation since the chain scission kinetic
equations were not taken into account in the previous works that reports a nucleation
mechanism.
The successful fitting of cellulose thermal degradation to a random scission model also implies
that the cellulosic polymer bonds are broken following first order kinetics because the random
scission model is derived from Simha-Wall equations (Simha and Wall 1952), which were
developed assuming random breakage of bonds and first order kinetics. Thus, the model
proposed in this work for the thermal degradation of cellulose allows the correlation of
macroscopic observations (overall mass loss) with the microscopic behaviour of the material
(rate of bond scission). However, it should be taken into account that the model does not
make any assumption whatsoever regarding the exact chemical nature of the bond breakage.
Conclusions
This paper brings the kinetics of cellulose thermal depolymerisation up to date by a careful
reassessment of current interpretations of the experimental data suggesting that cellulose
10
degradation follows an Avrami-Erofeev nucleation and growth mechanism. A detailed kinetic
analysis of cellulose pyrolysis has been carried out by means of the recently proposed
combined kinetic analysis method and the use of generalized master plots. These procedures
imply no assumption whatsoever regarding the kinetic model obeyed by the reaction thereby
avoiding the risks of model-fitting the experimental data with an improper kinetic model. The
results yielded by the analysis have been compared with a novel kinetic model involving a
chain scission mechanism. It has been demonstrated that the chain scission model fit the
experimental data more closely than the nucleation-like ones and, at the same time, explain
more appropriately cellulose depolymerisation mechanism. The kinetic parameters obtained
by the combined analysis can be used to reconstruct experimental curves recorded under
different heating profiles and to predict more accurately the behaviour of the system in
conditions different from the experimental ones.
Acknowledgments Financial support from projects TEP-03002 from Junta de Andalucía and
MAT 2008-06619/MAT from the Spanish Ministerio de Ciencia e Innovación is acknowledged.
11
References
Agrawal RK (1988a) Kinetics of reactions involved in pyrolysis of cellulose.1. The 3-reaction
model. Can J Chem Eng 66(3):403–412
Agrawal RK (1988b) Kinetics of reactions involved in pyrolysis of cellulose.2. The modified
Kilzer-Broido Model. Can J Chem Eng 66(3):413–418
Antal MJ, Varhegyi G, Jakab E (1998) Cellulose pyrolysis kinetics: revisited. Ind Eng Chem Res
37(4):1267–1275
Arii T, Ichihara S, Nakagawa H, Fujii N (1998) A kinetic study of the thermal decomposition of
polyesters by controlled-rate thermogravimetry. Thermochim Acta 319(1–2):139–149
Barneto A, Carmona J, Alfonso JE, Alcaide L (2009) Use of autocatalytic kinetics to obtain
composition of lignocellulosic materials. Bioresour Technol 100(17):3963–3973
Bigger SW, Scheirs J, Camino G (1998) An investigation of the kinetics of cellulose degradation
under non-isothermal conditions. Polym Degrad Stab 62(1):33–40
Bradbury AGW, Sakai Y, Shafizadeh F (1979) Kinetic model for pyrolysis of cellulose. J Appl
Polym Sci 23(11):3271–3280
Calvini P (2005) The influence of levelling-off degree of polymerisation on the kinetics of
cellulose degradation. Cellulose 12(4):445–447
Calvini P (2008) Comments on the article “On the degradation evolution equations of
cellulose” by Hongzhi Ding and Zhongdong Wang. Cellulose 15(2):225–228
Calvini P, Gorassini A, Merlani AL (2008) On the kinetics of cellulose degradation: looking
beyond the pseudo zero order rate equation. Cellulose 15(2):193–203
Capart R, Khezami L, Burnham AK (2004) Assessment of various kinetic models for the pyrolysis
of a microgranular cellulose. Thermochim Acta 417(1):79–89
Criado JM, Morales J (1976) Defects of thermogravimetric analysis for Discerning Between 1st
order reactions and those taking place through Avrami-Erofeevs mechanism. Thermochim Acta
16(3):382–387
Criado JM, Morales J (1977) Thermal decomposition reactions of solids controlled by diffusion
and phase-boundary processes—possible misinterpretation from thermogravimetric data.
Thermochim Acta 19(3):305–317
Criado JM, Perez-Maqueda LA, Gotor FJ, Malek J, Koga N (2003) A unified theory for the kinetic
analysis of solid state reactions under any thermal pathway. J Therm Anal Calorim 72(3):901–
12
906
Criado JM, Sanchez-Jimenez PE, Perez-Maqueda LA (2008) Critical study of the isoconversional
methods of kinetic analysis. J Therm Anal Calorim 92(1):199–203
Ding HZ, Wang ZD (2008a) Author response to the comments by P. Calvini regarding the article
“On the degradation evolution equations of cellulose” by H.-Z. Ding and Z. D. Wang. Cellulose
15(2):229–237
Ding HZ, Wang ZD (2008b) On the degradation evolution equations of cellulose. Cellulose
15(2):205–224
Dollimor D, Holt B (1973) Thermal degradation of cellulose in nitrogen. J Polym Sci Part B
Polym Phys 11(9):1703–1711
Emsley AM (2008) Cellulosic ethanol re-ignites the fire of cellulose degradation. Cellulose
15(2):187–192
Ganster J, Fink HP (2006) Novel cellulose fibre reinforced thermoplastic materials. Cellulose
13(3):271–280
Kilzer FJ, Broido A (1965) Speculation on the nature of cellulose pyrolysis. Pyrodynamics 2:151–
163
Koga N, Criado JM (1998) The influence of mass transfer phenomena on the kinetic analysis for
the thermal decomposition of calcium carbonate by constant rate thermal analysis (CRTA)
under vacuum. Int J Chem Kinet 30(10):737–744
Lin YC, Cho J, Tompsett GA, Westmoreland PR, Huber GW (2009) Kinetics and mechanism of
cellulose pyrolysis. J Phys Chem C 113(46):20097–20107
Liu HY, Liu DG, Yao F, Wu QL (2010) Fabrication and properties of transparent
polymethylmethacrylate/cellulose nanocrystals composites. Bioresour Technol 101(14):5685–
5692
Mamleev V, Bourbigot S, Le Bras M, Yvon J, Lefebvre J (2006) Model-free method for
evaluation of activation energies in modulated thermogravimetry and analysis of cellulose
decomposition. Chem Eng Sci 61(4):1276–1292
Mamleev V, Bourbigot S, Yvon J (2007a) Kinetic analysis of the thermal decomposition of
cellulose: the change of the rate limitation. J Anal Appl Pyrol 80(1):141–150
Mamleev V, Bourbigot S, Yvon J (2007b) Kinetic analysis of the thermal decomposition of
cellulose: the main step of mass loss. J Anal Appl Pyrol 80(1):151–165
13
Mamleev V, Bourbigot S, Le Bras M, Yvon J (2009) The facts and hypotheses relating to the
phenomenological model of cellulose pyrolysis Interdependence of the steps. J Anal Appl Pyrol
84(1):1–17
Mohan D, Pittman CU, Steele PH (2006) Pyrolysis of wood/biomass for bio-oil: a critical review.
Energy Fuels 20(3):848–889
PerezMaqueda LA, Ortega A, Criado JM (1996) The use of master plots for discriminating the
kinetic model of solid state reactions from a single constant-rate thermal analysis (CRTA)
experiment. Thermochim Acta 277:165–173
Perez-Maqueda LA, Criado JM, Subrt J, Real C (1999) Synthesis of acicular hematite catalysts
with tailored porosity. Catal Lett 60(3):151–156
Perez-Maqueda LA, Criado JM, Gotor FJ (2002a) Controlled rate thermal analysis commanded
by mass spectrometry for studying the kinetics of thermal decomposition of very stable solids.
Int J Chem Kinet 34(3):184–192
Perez-Maqueda LA, Criado JM, Gotor FJ, Malek J (2002b) Advantages of combined kinetic
analysis of experimental data obtained under any heating profile. J Phys Chem A
106(12):2862–2868
Perez-Maqueda LA, Criado JM, Malek J (2003) Combined kinetic analysis for crystallization
kinetics of non-crystalline solids. J Non-Cryst Solids 320(1–3):84–91
Perez-Maqueda LA, Criado JM, Sanchez-Jimenez PE (2006) Combined kinetic analysis of solidstate reactions: a powerful tool for the simultaneous determination of kinetic parameters and
the kinetic model without previous assumptions on the reaction mechanism. J Phys Chem A
110(45):12456–12462
Reynolds JG, Burnham AK (1997) Pyrolysis decomposition kinetics of cellulose-based materials
by constant heating rate micropyrolysis. Energy Fuels 11(1):88–97
Rouquerol J (2003) A general introduction to SCTA and to rate-controlled SCTA. J Therm Anal
Calorim 72(3):1081–1086
Saddawi A, Jones JM, Williams A, Wojtowicz MA (2010) Kinetics of the Thermal Decomposition
of Biomass. Energy Fuels 24:1274–1282
Sanchez-Jimenez PE, Perez-Maqueda LA, Perejon A, Criado JM (2009) Combined kinetic
analysis of thermal degradation of polymeric materials under any thermal pathway. Polym
Degrad Stab 94(11):2079–2085
Sanchez-Jimenez PE, Perejon A, Criado JM, Dianez MJ, Perez-Maqueda LA (2010a) Kinetic
model for thermal dehydrochlorination of poly(vinyl chloride). Polymer 51(17):3998–4007
14
Sanchez-Jimenez PE, Perez-Maqueda LA, Crespo-Amoros JE, Lopez J, Perejon A, Criado JM
(2010b) Quantitative characterization of multicomponent polymers by sample-controlled
thermal analysis. Anal Chem 82(21):8875–8880
Sanchez-Jimenez PE, Perez-Maqueda LA, Perejon A, Criado JM (2010c) A new model for the
kinetic analysis of thermal degradation of polymers driven by random scission. Polym Degrad
Stab 95(5):733–739
Sánchez-Jiménez PE, Pérez-Maqueda LA, Perejón A, Criado JM (2011) Constant rate thermal
analysis fot thermal stability studies of polymers. Polym Degrad Stab 96(5):974–981
Sestak J, Berggren G (1971) Study of the kinetics of the mechanism of solid-state reactions at
increased temperature. Thermochim Acta 3:1–12
Shen DK, Gu S (2009) The mechanism for thermal decomposition of cellulose and its main
products. Bioresour Technol 100(24):6496–6504
Simha R, Wall LA (1952) Kinetics of chain depolymerization. J Phys Chem 56(6):707–715
Varhegyi G, Jakab E, Antal MJ (1994) Is the Broido-Shafizadeh model for cellulose true? Energy
Fuels 8(6):1345–1352
Volker S, Rieckmann T (2002) Thermokinetic investigation of cellulose pyrolysis—impact of
initial and final mass on kinetic results. J Anal Appl Pyrol 62(2):165–177
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Table 1 f(α) kinetic functions for the most widely used kinetic models, including the newly
proposed random scission model
Mechanism
Symbol
Phase boundary controlled reaction (contracting area)
R2
Phase boundary controlled reaction (contracting volume)
R3
f(α)
Random nucleation followed by an instantaneous growth of
F1
nuclei. (Avrami-Erofeev eqn. n = 1)
Random nucleation and growth of nuclei through different
nucleation and nucleus growth models. (Avrami-Erofeev eq. An
n ≠ 1)
Two-dimensional diffusion
D2
Three-dimensional diffusion (Jander equation)
D3
Three-dimensional
equation)
D4
diffusion
(Ginstling-Brounshtein
Random Scission L = 2
L2
Random Scission L > 2
Ln
No symbolic solution
16
Table 2 Activation energy values for different values of conversion and their correlation
coefficients, obtained by the Friedman isoconversional analysis of the curves showed in
Fig. 1
α
r
Ea (kJ mol−1)
0.1 0.997 191 ± 6
0.2 0.998 192 ± 4
0.3 0.999 192 ± 4
0.4 0.999 192 ± 4
0.5 0.999 191 ± 4
0.6 0.999 190 ± 4
0.7 0.999 190 ± 4
0.8 0.999 190 ± 4
0.9 0.831 119 ± 32
17
Figure captions
Figure 1. Experimental curves (dotted lines) obtained for the thermal decomposition of
microcrystalline cellulose under N2 gas flow and the following experimental conditions: a linear
heating rate of 1, 2, 5 and 10 K min−1; b isotherm at 533 and 548 K; and c CRTA degradation
rate of 0.006 and 0.009 min−1. Solid lines represents the curves reconstructed assuming the
kinetic parameters calculated by the combined analysis method: n = 1.300, m = 0.392,
E = 193 kJ mol−1 and A = 5.9 1016 min−1
Figure 2. Plot of the reaction rate against the conversion α for the isothermal experiments run
at 548 and 533 K. The maximum in both cases is close to that expected for chain scission
models
Figure 3. Experimental temperature (solid line) and degree of conversion (dotted line), against
time plots, as obtained from the thermal decomposition of cellulose under CRTA conditions.
The degradation rate was set at a constant value of 0.009 min−1 and the experiment performed
under an inert nitrogen atmosphere. The inset shows a detail of the temperature versus
conversion curve, with a minimum at α = 0.25
Figure 4. Combined kinetic analysis of the experimental curves included in Fig. 1 for the results
of the optimization procedure of Eq. 9, that is n = 1.300, m = 0.392, E = 193 kJ mol−1 and A = 5.9
1016 min−1
Figure 5. Comparison of the f(α) functions (lines) normalized at α = 0.5 corresponding to some
of the ideal kinetic models included in Table 1 with the reduced Sestak-Berggren equation
(squares) considering the parameters n and m calculated by means of the Eq. 9 for cellulose
pyrolysis
Figure 6. Scheme illustrating the initial steps of cellulose depolymerisation assuming a chain
scission mechanism
18
Figure 1
19
Figure 2
20
Figure 3
21
Figure 4
22
Figure 5
23
Figure 6
24